Precalculus Flashcard 10 (Fall Semester Review)

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They are the x-intercepts of the graph of the polynomial.

Front

How do you determine the correct equation for a graphed polynomial?

Back

To determine the correct equation, analyze the graph's intercepts, end behavior, and multiplicity of roots, then match these characteristics to the given options.

Front

What is end behavior in polynomials?

Back

End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What is the leading term of a polynomial?

Back

The leading term is the term in a polynomial with the highest degree. It determines the end behavior of the polynomial.

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) = y, then the inverse function f^(-1)(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

Front

What are asymptotes in a function?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the function is undefined, typically where the denominator of a rational function equals zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote indicates the behavior of a function as x approaches infinity. It is found by analyzing the degrees of the numerator and denominator.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is the ratio of two polynomials.